Internal problem ID [11024]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 6.4 Reduction to a single ODE. Problems page 415
Problem number: Problem 4(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {2 t}{7}+\frac {y \left (t \right )}{7}\\ y^{\prime }\left (t \right )&=-\frac {3 t}{7}+\frac {2 y \left (t \right )}{7} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve([2*diff(x(t),t)-diff(y(t),t)=t,3*diff(x(t),t)+2*diff(y(t),t)=y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {t^{2}}{4}+\frac {3 t}{4}+\frac {{\mathrm e}^{\frac {2 t}{7}} c_{2}}{2}+c_{1} \] \[ y \left (t \right ) = \frac {3 t}{2}+\frac {21}{4}+{\mathrm e}^{\frac {2 t}{7}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 56
DSolve[{2*x'[t]-y'[t]==t,3*x'[t]+2*y'[t]==y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{8} \left (2 t (t+3)+4 c_2 \left (e^{2 t/7}-1\right )+21+8 c_1\right ) \\ y(t)\to \frac {3 t}{2}+c_2 e^{2 t/7}+\frac {21}{4} \\ \end{align*}